2 Structure. 2.1 Coulomb interactions

Size: px
Start display at page:

Download "2 Structure. 2.1 Coulomb interactions"

Transcription

1 2 Structure 2.1 Coulomb interactions While the information needed for reproduction of living systems is chiefly maintained in the sequence of macromolecules, any practical use of this information must rely on the physical forces that shape the molecules into functioning, sequence-dependent, structures. These forces and the resulting structures are the topic of the second segment of this course. Since neither gravity, nor nuclear interactions, are particularly relevant to most organisms, the forces that shape the molecules of life are various manifestations of the electromagnetic interactions between electrons and nuclei. These include the strong covalent bonds (maintaining the primary connectivity of a molecule), the weaker hydrogen bonds (sensitive to orientations of the participating moieties), and the even weaker (and roughly direction independent) van der Waals forces. However, for these molecules to properly fold and function in the cell environment, their functionally relevant energy scales should be of the order of the thermal energy k B T at room temperature. Higher energies would freeze the corresponding degrees of freedom, while lower energies would be irrelevant and ignored in comparison to the ubiquitous thermal fluctuations. Thus entropic considerations play a major role in biomolecules, as will be emphasized in the much simpler systems considered in the following sections Charge dissociation in solution Entropy is indeed the reason why many molecules (electrolytes) dissociate and ionize in solution. The opposing charges making up an ion clearly minimize the Coulomb energy by being in close proximity in a bound (molecular) state. The loss of this electrostatic energy in the dissociated (ionized) state is balanced by the gain in configurational entropy. We can quantify this by an approximate evaluation of the change in free energy upon dissociation, as ( ) V F = E T S = E b + k B T log. (2.1) Nv 0 Here, E b is the binding energy, T is the temperature, k B is the Boltzmann constant, and v 0 is some characteristic volume. The gain in entropy is estimated from the number of positions available for each of N particles in the volume V. In a more systematic evaluation of the partition function, v 0 = λ 3, where λ is the thermal wavelength. Setting the free energy change to zero, gives the equilibrium concentration c = N V = 1 λ 3e βe b. (2.2) The electrostaic contribution to the binding energy, E c, can be computed from Coulomb s law, as E c = q 1q 2 ǫr = e2 z 2 ǫr, (2.3) 27

2 where ǫ denotes the dielectric constant of water, z is the valence, and e is the electron charge. The physically significant quantity is the ratio of this energy to the thermal energy k B T, which can be expressed as βe c = βe2 z 2 = z 2l B ǫr r, (2.4) where we have defined the Bjerrum length l B = e2 ǫk B T. (2.5) For water, ǫ 81, and the Bjerrum length is about 7.1 Å. Very roughly, we can say that at separations larger than l B, the Coulomb interaction between unit charges in water is insignificant compared to thermal energy. We can also think of dissociation as the chemical reaction CA C + + A. (2.6) (The dissociated positive charge is called a cation, the negative one an anion.) The equilibrium constant of the reaction K eq. [C +][A ] e βe b, (2.7) [CA] is a measure of the ease with which ionization occurs. For strong electrolytes, such as Na + Cl (salt), Na + OH (base) and H + Cl (acid), which dissociate almost totally, the net binding energy is small. Weaker electrolytes are more strongly bound and dissociate less readily. Water itself can dissociate into H + and OH ions, but at room temperature this process only produces about 10 7 hydrogen ions per mole. 28

3 Biological molecules also dissociate, and the charge environment of a cell is quite complicated. The lipids forming the cell membrane become negatively charged upon dissociation, as does DNA. The latter is an acid that releases H + ions, leaving behind a negatively charged backbone. Proteins can also release H + ions, but some of the amino-acid side groups are actually basic, releasing OH. A molecule of this sort, which can develop regions both of positive and of negative charge upon dissociation, is called a polyampholyte. Molecules like the DNA backbone, which carry a uniform charge, are known as polyelectrolytes. Together, both sorts of macromolecules are referred to as macroions, and the small charged particles they give up into the cytoplasm are called counterions. The electrostatic interactions between the macromolecules are very important for their biological function the repulsive forces prevent aggregation, while attractions are important for docking and recognition. However, calculating these interactions in the environment of the moving counterions is not an easy task The Poisson Boltzmann Equation We know that proteins bind to one another, and that some proteins bind to DNA. In principle, an effective interaction between such macroions can be obtained by holding them at fixed separation (and orientation). A constrained partition function is then evaluated by integrating over all the other degrees of freedom, e.g. the positions of the more mobile counterions, as e βf(macroions) = Zres. = d 3 r i e βhc. (2.8) In addition to steric constraints (the excluded volume around each atom), the Hamiltonian H c includes the direct Coulomb interactions between the macroions, their interactions with the counterions, as well as the interactions amongst counterions. The restricted partition function is too hard to compute directly, and we shall instead resort to a mean-field approximation in which each counterion is assumed to experience an effective potential φ( r) due to the macroion, as well as all the other counterions. The effective potential is then computed self-consistently. In this approximation, the position-dependent density of counterion species α adjusts to the potential through the Boltzmann weight, as i n α ( r) = n α exp [ βφ( r)z α e]. (2.9) Note that n α is in general not the particle density, but an overall parameter that needs to be adjusted so that the integral over r leads to the correct number of counterions. The potential φ( r) is in turn determined by the charge distribution, and satisfies the Poisson equation. 2 φ = 4π ǫ ρ( r). (2.10) The charge density at each point has a contribution from the macroions, and from the 29

4 (fluctuation averaged) counterion density, and thus ρ( r) = ρ macroions ( r) + α z α e n α e βφzαe. (2.11) Self-consistency then leads to the Poisson-Boltzmann Equation [ 2 φ = 4π ρ macroions ( r) + ] z α e n α e βφzαe, (2.12) ǫ α This equation, while a drastic simplification of the original problem, is commonly used. It is a non-linear partial differential equation, and exact solutions are available only for a few simple geometries. It does have the virtue of being at least numerically solvable Debye screening by salt ions We expect physically that counterions will accumulate near regions of opposite charge to lower the electrostatic energy. As a result a charged macroion will be surrounded by a cloud of counterions, shielding and reducing its net charge. This effect is easily captured in a linearized version of Eq. (2.12). Linearizing the Boltzmann weight is actually a quite good approximation when the Coulomb interaction between macroions is screened by a high concentration of salt ions. The first step is to expand the exponential such that the local counterion charge density is z α n α e βzαeφ z α n α [1 βz α eφ + ]. (2.13) α α We note that at this order the local variations in counterion charge density and potential are simply proportional. Since the salt ions are overall neutral, we can then identify n α with the overall particle density of species α at this order. The condition of charge neutrality, α z α n α = 0, then leads to where λ 2 = α 2 φ = 4π ǫ ρ macro( r) + φ λ2, (2.14) 4π ǫ βe2 z α n 2 α = 4πl B z α n 2 α. (2.15) This is the Debye-Hückel equation, and the parameter λ is the Debye screening length. In a typical biological environment λ is around 1nm. For the case of a point charge Q = ze, i.e. for α ρ macro ( r) = zeδ 3 (r), (2.16) 30

5 the solution is the exponentially damped version of the Coulomb potential φ( r) = k B T zl B r r e λ. (2.17) Since Eq. (2.14) is linear, its solution for a general distribution of charges is obtained by simple superposition, leading to the interaction energy Dissociation from a plate βe interactions (macroions) = l B m<n z m z n rmn r mn e λ. (2.18) Let us now consider the full Poisson Boltzmann equation for the simple geometry of a flat plate, e.g. describing a membrane. Upon dissociation the membrane is negatively charged; its charge density denoted by σ = e/d 2 (i.e. ignoring discreteness effects, the negative charges are on average a distance d apart). The neutralizing counterions, of charge +e are present in the solution on both sides of the membrane. Due to translational symmetry, the average charge density (and potential) only depend on the separation from the plate, indicated by the coordinate y, and Eq. (2.12) now reads d 2 φ dy 2 = 4π ǫ e ne βeφ(y). (2.19) The following trick allows us to guess the solution to Eq. (2.19). We first make a transformation to W(y) = e βeφ/2 = φ = 2 log W, (2.20) βe such that φ = 2 W βe W, and φ = 2 βe W W W 2. W 2 Multiplying both sides by W 2, Eq. (2.19) can be recast as 2 ( W W W 2) = 4π βe ǫ 31 e n. (2.21)

6 While still non-linear, it is easy to see that a linear function of y satisfies the above equation, and we set W(y) = 1 + y y 0, (2.22) where we have arbitrarily set φ(y 0) = 0, such that W(0) = 1, and y0 2 = 2πβe 2 n/ǫ. Note, however that n is simply a parameter that needs to be set by the requirement of charge neutrality. It is easier to trade in this parameter for y 0 and constrain the latter. The electrostatic potential thus has the form φ(y) = 2 βe log [1 + yy0 ]. (2.23) The undetermined length y 0, clearly sets the scale at which the counterion density changes significantly. It can be determined by examining the limit y y 0, for which Eq. (2.23) becomes φ(y) 2 y. (2.24) βe y 0 Indeed, at distances close enough to the surface that screening is unimportant, we expect the electric field to be (e.g. by appealing to a Gaussian pillbox) E = 2πσ ǫ, and a corresponding potential φ = 2πσ ǫ y. (2.25) Comparing this result with Eq. (2.24) indicates that y 0 = ǫ eσπβ = ǫ d 2 βe 2 π = d2. (2.26) πl B This characteristic scale is known as the Guoy-Chapman length, characterizing the thickness of the diffusive boundary layer of ions that shields a charged membrane. Retracing the steps of algebra, it is easy to check that and n = π 2 n(y) = n W 2 = π 2 l B d 4, ( l B 1 + y ) 2. (2.27) d 4 y 0 At large separations, y y 0 from the plate, the counterion density falls off as (2πl B y 2 ) 1. The corresponding potential behaves as φ(y) 2 ln(y)/(βe), very different from the linear potential in vacuum, and also quite distinct from an exponential decay that may have been surmised based on Debye-Huckel screening. Clearly this type of screening will lead to a quite 32

7 different interaction between charged plates, a question that will be taken up in the next problem set. In connection to that, we note that Eq. (2.21) also admits solutions of the form cos(y/y 1 + θ) with parameters y 1 and θ that can be adjusted to conform to the boundary conditions corresponding to parallel charged plates. While the solutions to the Poisson-Boltzmann equation are interesting and informative, they do not capture the entire physics of the problem. Fluctuations in charge density can be important in lowering the free energy. Indeed at high temperatures the correlated fluctuations around two similarly charged macroions further reduce the repulsion through a dipole-dipole interaction reminiscent of the van der Waals force. If strong enough these fluctuations can entirely reverse the sign of the force, leading to an attractive interaction between like-charged macroions. Such phenomena, not captured by the Poisson-Boltzmann equation, have received considerable attention in recent years. 33

8

8.592J HST.452J: Statistical Physics in Biology

8.592J HST.452J: Statistical Physics in Biology Assignment # 4 8.592J HST.452J: Statistical Physics in Biology Coulomb Interactions 1. Flory Theory: The Coulomb energy of a ball of charge Q and dimension R in d spacial dimensions scales as Q 2 E c.

More information

Proteins polymer molecules, folded in complex structures. Konstantin Popov Department of Biochemistry and Biophysics

Proteins polymer molecules, folded in complex structures. Konstantin Popov Department of Biochemistry and Biophysics Proteins polymer molecules, folded in complex structures Konstantin Popov Department of Biochemistry and Biophysics Outline General aspects of polymer theory Size and persistent length of ideal linear

More information

The change in free energy on transferring an ion from a medium of low dielectric constantε1 to one of high dielectric constant ε2:

The change in free energy on transferring an ion from a medium of low dielectric constantε1 to one of high dielectric constant ε2: The Born Energy of an Ion The free energy density of an electric field E arising from a charge is ½(ε 0 ε E 2 ) per unit volume Integrating the energy density of an ion over all of space = Born energy:

More information

V = 2ze 2 n. . a. i=1

V = 2ze 2 n. . a. i=1 IITS: Statistical Physics in Biology Assignment # 3 KU Leuven 5/29/2013 Coulomb Interactions & Polymers 1. Flory Theory: The Coulomb energy of a ball of charge Q and dimension R in d spacial dimensions

More information

Module 8: "Stability of Colloids" Lecture 38: "" The Lecture Contains: Calculation for CCC (n c )

Module 8: Stability of Colloids Lecture 38:  The Lecture Contains: Calculation for CCC (n c ) The Lecture Contains: Calculation for CCC (n c ) Relation between surface charge and electrostatic potential Extensions to DLVO theory file:///e /courses/colloid_interface_science/lecture38/38_1.htm[6/16/2012

More information

Aqueous solutions. Solubility of different compounds in water

Aqueous solutions. Solubility of different compounds in water Aqueous solutions Solubility of different compounds in water The dissolution of molecules into water (in any solvent actually) causes a volume change of the solution; the size of this volume change is

More information

Multimedia : Boundary Lubrication Podcast, Briscoe, et al. Nature , ( )

Multimedia : Boundary Lubrication Podcast, Briscoe, et al. Nature , ( ) 3.05 Nanomechanics of Materials and Biomaterials Thursday 04/05/07 Prof. C. Ortiz, MITDMSE I LECTURE 14: TE ELECTRICAL DOUBLE LAYER (EDL) Outline : REVIEW LECTURE #11 : INTRODUCTION TO TE ELECTRICAL DOUBLE

More information

Physical Chemistry - Problem Drill 01: Chemistry and Physics Review

Physical Chemistry - Problem Drill 01: Chemistry and Physics Review Physical Chemistry - Problem Drill 01: Chemistry and Physics Review No. 1 of 10 1. Chemical bonds are considered to be the interaction of their electronic structures of bonding atoms involved, with the

More information

Bchem 675 Lecture 9 Electrostatics-Lecture 2 Debye-Hückel: Continued Counter ion condensation

Bchem 675 Lecture 9 Electrostatics-Lecture 2 Debye-Hückel: Continued Counter ion condensation Bchem 675 Lecture 9 Electrostatics-Lecture 2 Debye-Hückel: Continued Counter ion condensation Ion:ion interactions What is the free energy of ion:ion interactions ΔG i-i? Consider an ion in a solution

More information

Lectures 11-13: Electrostatics of Salty Solutions

Lectures 11-13: Electrostatics of Salty Solutions Lectures 11-13: Electrostatics of Salty Solutions Lecturer: Brigita Urbanc Office: 1-909 (E-mail: brigita@drexel.edu) Course website: www.physics.drexel.edu/~brigita/courses/biophys_011-01/ 1 Water as

More information

CHAPTER 2 INTERATOMIC FORCES. atoms together in a solid?

CHAPTER 2 INTERATOMIC FORCES. atoms together in a solid? CHAPTER 2 INTERATOMIC FORCES What kind of force holds the atoms together in a solid? Interatomic Binding All of the mechanisms which cause bonding between the atoms derive from electrostatic interaction

More information

Atoms & Their Interactions

Atoms & Their Interactions Lecture 2 Atoms & Their Interactions Si: the heart of electronic materials Intel, 300mm Si wafer, 200 μm thick and 48-core CPU ( cloud computing on a chip ) Twin Creeks Technologies, San Jose, Si wafer,

More information

Electrolytes. Chapter Basics = = 131 2[ ]. (c) From both of the above = = 120 8[

Electrolytes. Chapter Basics = = 131 2[ ]. (c) From both of the above = = 120 8[ Chapter 1 Electrolytes 1.1 Basics Here we consider species that dissociate into positively and negatively charged species in solution. 1. Consider: 1 H (g) + 1 Cl (g) + ()+ () = { } = (+ )+ ( ) = 167[

More information

Solutions and Non-Covalent Binding Forces

Solutions and Non-Covalent Binding Forces Chapter 3 Solutions and Non-Covalent Binding Forces 3.1 Solvent and solution properties Molecules stick together using the following forces: dipole-dipole, dipole-induced dipole, hydrogen bond, van der

More information

Molecular Modeling -- Lecture 15 Surfaces and electrostatics

Molecular Modeling -- Lecture 15 Surfaces and electrostatics Molecular Modeling -- Lecture 15 Surfaces and electrostatics Molecular surfaces The Hydrophobic Effect Electrostatics Poisson-Boltzmann Equation Electrostatic maps Electrostatic surfaces in MOE 15.1 The

More information

Structural Bioinformatics (C3210) Molecular Mechanics

Structural Bioinformatics (C3210) Molecular Mechanics Structural Bioinformatics (C3210) Molecular Mechanics How to Calculate Energies Calculation of molecular energies is of key importance in protein folding, molecular modelling etc. There are two main computational

More information

Name Date. Chapter 2 - Chemistry Guide Microbiology (MCB 2010C) Part 1

Name Date. Chapter 2 - Chemistry Guide Microbiology (MCB 2010C) Part 1 Name Date Chapter 2 - Chemistry Guide Microbiology (MCB 2010C) Part 1 The study of biology in the 21 st century is actually the study of biochemistry. In order to be successful in this course, it is important

More information

Lattice energy of ionic solids

Lattice energy of ionic solids 1 Lattice energy of ionic solids Interatomic Forces Solids are aggregates of atoms, ions or molecules. The bonding between these particles may be understood in terms of forces that play between them. Attractive

More information

INTERMOLECULAR AND SURFACE FORCES

INTERMOLECULAR AND SURFACE FORCES INTERMOLECULAR AND SURFACE FORCES SECOND EDITION JACOB N. ISRAELACHVILI Department of Chemical & Nuclear Engineering and Materials Department University of California, Santa Barbara California, USA ACADEMIC

More information

Chapter 3. Crystal Binding

Chapter 3. Crystal Binding Chapter 3. Crystal Binding Energy of a crystal and crystal binding Cohesive energy of Molecular crystals Ionic crystals Metallic crystals Elasticity What causes matter to exist in three different forms?

More information

Chapter 02 The Chemical Basis of Life I: Atoms, Molecules, and Water

Chapter 02 The Chemical Basis of Life I: Atoms, Molecules, and Water Chapter 02 The Chemical Basis of Life I: Atoms, Molecules, and Water Multiple Choice Questions 1. The atomic number of an atom is A. the number of protons in the atom. B. the number of neutrons in the

More information

Chapter 2 - Water 9/8/2014. Water exists as a H-bonded network with an average of 4 H-bonds per molecule in ice and 3.4 in liquid. 104.

Chapter 2 - Water 9/8/2014. Water exists as a H-bonded network with an average of 4 H-bonds per molecule in ice and 3.4 in liquid. 104. Chapter 2 - Water Water exists as a -bonded network with an average of 4 -bonds per molecule in ice and 3.4 in liquid. 104.5 o -bond: An electrostatic attraction between polarized molecules containing

More information

schematic diagram; EGF binding, dimerization, phosphorylation, Grb2 binding, etc.

schematic diagram; EGF binding, dimerization, phosphorylation, Grb2 binding, etc. Lecture 1: Noncovalent Biomolecular Interactions Bioengineering and Modeling of biological processes -e.g. tissue engineering, cancer, autoimmune disease Example: RTK signaling, e.g. EGFR Growth responses

More information

The effect of surface dipoles and of the field generated by a polarization gradient on the repulsive force

The effect of surface dipoles and of the field generated by a polarization gradient on the repulsive force Journal of Colloid and Interface Science 263 (2003) 156 161 www.elsevier.com/locate/jcis The effect of surface dipoles and of the field generated by a polarization gradient on the repulsive force Haohao

More information

Lecture 3 Charged interfaces

Lecture 3 Charged interfaces Lecture 3 Charged interfaces rigin of Surface Charge Immersion of some materials in an electrolyte solution. Two mechanisms can operate. (1) Dissociation of surface sites. H H H H H M M M +H () Adsorption

More information

16 years ago TODAY (9/11) at 8:46, the first tower was hit at 9:03, the second tower was hit. Lecture 2 (9/11/17)

16 years ago TODAY (9/11) at 8:46, the first tower was hit at 9:03, the second tower was hit. Lecture 2 (9/11/17) 16 years ago TODAY (9/11) at 8:46, the first tower was hit at 9:03, the second tower was hit By Anthony Quintano - https://www.flickr.com/photos/quintanomedia/15071865580, CC BY 2.0, https://commons.wikimedia.org/w/index.php?curid=38538291

More information

The Logic of Biological Phenomena

The Logic of Biological Phenomena The Logic of Biological Phenomena molecules are lifeless yet, in appropriate complexity and number, molecules compose living things What makes living things distinct? they can grow they can move they can

More information

The broad topic of physical metallurgy provides a basis that links the structure of materials with their properties, focusing primarily on metals.

The broad topic of physical metallurgy provides a basis that links the structure of materials with their properties, focusing primarily on metals. Physical Metallurgy The broad topic of physical metallurgy provides a basis that links the structure of materials with their properties, focusing primarily on metals. Crystal Binding In our discussions

More information

Soft Matter - Theoretical and Industrial Challenges Celebrating the Pioneering Work of Sir Sam Edwards

Soft Matter - Theoretical and Industrial Challenges Celebrating the Pioneering Work of Sir Sam Edwards Soft Matter - Theoretical and Industrial Challenges Celebrating the Pioneering Work of Sir Sam Edwards One Hundred Years of Electrified Interfaces: The Poisson-Boltzmann theory and some recent developments

More information

Water, water everywhere,; not a drop to drink. Consumption resulting from how environment inhabited Deforestation disrupts water cycle

Water, water everywhere,; not a drop to drink. Consumption resulting from how environment inhabited Deforestation disrupts water cycle Chapter 3 Water: The Matrix of Life Overview n n n Water, water everywhere,; not a drop to drink Only 3% of world s water is fresh How has this happened Consumption resulting from how environment inhabited

More information

Lecture 5: Electrostatic Interactions & Screening

Lecture 5: Electrostatic Interactions & Screening Lecture 5: Electrostatic Interactions & Screening Lecturer: Prof. Brigita Urbanc (brigita@drexel.edu) PHYS 461 & 561, Fall 2009-2010 1 A charged particle (q=+1) in water, at the interface between water

More information

`1AP Biology Study Guide Chapter 2 v Atomic structure is the basis of life s chemistry Ø Living and non- living things are composed of atoms Ø

`1AP Biology Study Guide Chapter 2 v Atomic structure is the basis of life s chemistry Ø Living and non- living things are composed of atoms Ø `1AP Biology Study Guide Chapter 2 v Atomic structure is the basis of life s chemistry Ø Living and non- living things are composed of atoms Ø Element pure substance only one kind of atom Ø Living things

More information

Chapter 1. Topic: Overview of basic principles

Chapter 1. Topic: Overview of basic principles Chapter 1 Topic: Overview of basic principles Four major themes of biochemistry I. What are living organism made from? II. How do organism acquire and use energy? III. How does an organism maintain its

More information

Mirror Charges, Hydrogen Bonds, And the Water-Dielectric Interface

Mirror Charges, Hydrogen Bonds, And the Water-Dielectric Interface Mirror Charges, ydrogen Bonds, And the Water-Dielectric Interface Kevin Cahill cahill@unm.edu http://dna.phys.unm.edu/ 1 Field Energy The energy E of an electric field E( x, t) is the space integral of

More information

Atoms, electrons and Solids

Atoms, electrons and Solids Atoms, electrons and Solids Shell model of an atom negative electron orbiting a positive nucleus QM tells that to minimize total energy the electrons fill up shells. Each orbit in a shell has a specific

More information

States of matter Part 1

States of matter Part 1 Physical pharmacy I 1. States of matter (2 Lectures) 2. Thermodynamics (2 Lectures) 3. Solution of non-electrolyte 4. Solution of electrolyte 5. Ionic equilibria 6. Buffered and isotonic solution Physical

More information

States of matter Part 1. Lecture 1. University of Kerbala. Hamid Alghurabi Assistant Lecturer in Pharmaceutics. Physical Pharmacy

States of matter Part 1. Lecture 1. University of Kerbala. Hamid Alghurabi Assistant Lecturer in Pharmaceutics. Physical Pharmacy Physical pharmacy I 1. States of matter (2 Lectures) 2. Thermodynamics (2 Lectures) 3. Solution of non-electrolyte 4. Solution of electrolyte 5. Ionic equilibria 6. Buffered and isotonic solution Physical

More information

Earth Solid Earth Rocks Minerals Atoms. How to make a mineral from the start of atoms?

Earth Solid Earth Rocks Minerals Atoms. How to make a mineral from the start of atoms? Earth Solid Earth Rocks Minerals Atoms How to make a mineral from the start of atoms? Formation of ions Ions excess or deficit of electrons relative to protons Anions net negative charge Cations net

More information

Complicated, short range. þq 1 Q 2 /4p3 0 r (Coulomb energy) Q 2 u 2 /6(4p3 0 ) 2 ktr 4. u 2 1 u2 2 =3ð4p3 0Þ 2 ktr 6 ðkeesom energyþ

Complicated, short range. þq 1 Q 2 /4p3 0 r (Coulomb energy) Q 2 u 2 /6(4p3 0 ) 2 ktr 4. u 2 1 u2 2 =3ð4p3 0Þ 2 ktr 6 ðkeesom energyþ Bonding ¼ Type of interaction Interaction energy w(r) Covalent, metallic Complicated, short range Charge charge þq 1 Q 2 /4p3 0 r (Coulomb energy) Charge dipole Qu cos q/4p3 0 r 2 Q 2 u 2 /6(4p3 0 ) 2

More information

6, Physical Chemistry -II (Statistical Thermodynamics, Chemical Dynamics, Electrochemistry and Macromolecules)

6, Physical Chemistry -II (Statistical Thermodynamics, Chemical Dynamics, Electrochemistry and Macromolecules) Subject Paper No and Title Module No and Title Module Tag 6, Physical -II (Statistical Thermodynamics, Chemical Dynamics, Electrochemistry and Macromolecules) 25, Activity and Mean Activity coefficient

More information

Fundamental Interactions: 6 Forces

Fundamental Interactions: 6 Forces Fundamental Interactions: 6 Forces In nuclear and high-energy physics 6 fundamental forces are recognized, which describe the structure of matter. - the strong interaction - the weak interaction act inside

More information

SAM Teachers Guide Chemical Bonds

SAM Teachers Guide Chemical Bonds SAM Teachers Guide Chemical Bonds Overview Students discover that the type of bond formed ionic, non polar covalent, or polar covalent depends on the electronegativity of the two atoms that are bonded

More information

Atomic structure & interatomic bonding. Chapter two

Atomic structure & interatomic bonding. Chapter two Atomic structure & interatomic bonding Chapter two 1 Atomic Structure Mass Charge Proton 1.67 х 10-27 kg + 1.60 х 10-19 C Neutron 1.67 х 10-27 kg Neutral Electron 9.11 х 10-31 kg - 1.60 х 10-19 C Electron

More information

On the Chemical Free Energy of the Electrical Double Layer

On the Chemical Free Energy of the Electrical Double Layer 1114 Langmuir 23, 19, 1114-112 On the Chemical Free Energy of the Electrical Double Layer Marian Manciu and Eli Ruckenstein* Department of Chemical Engineering, State University of New York at Buffalo,

More information

DEFINITION. The electrostatic force of attraction between oppositely charged ions

DEFINITION. The electrostatic force of attraction between oppositely charged ions DEFINITION The electrostatic force of attraction between oppositely charged ions Usually occurs when a metal bonds with a non-metal Ions are formed by complete electron transfer from the metal atoms to

More information

Module17: Intermolecular Force between Surfaces and Particles. Lecture 23: Intermolecular Force between Surfaces and Particles

Module17: Intermolecular Force between Surfaces and Particles. Lecture 23: Intermolecular Force between Surfaces and Particles Module17: Intermolecular Force between Surfaces and Particles Lecture 23: Intermolecular Force between Surfaces and Particles 1 We now try to understand the nature of spontaneous instability in a confined

More information

Biophysics II. Hydrophobic Bio-molecules. Key points to be covered. Molecular Interactions in Bio-molecular Structures - van der Waals Interaction

Biophysics II. Hydrophobic Bio-molecules. Key points to be covered. Molecular Interactions in Bio-molecular Structures - van der Waals Interaction Biophysics II Key points to be covered By A/Prof. Xiang Yang Liu Biophysics & Micro/nanostructures Lab Department of Physics, NUS 1. van der Waals Interaction 2. Hydrogen bond 3. Hydrophilic vs hydrophobic

More information

BIOCHEMISTRY GUIDED NOTES - AP BIOLOGY-

BIOCHEMISTRY GUIDED NOTES - AP BIOLOGY- BIOCHEMISTRY GUIDED NOTES - AP BIOLOGY- ELEMENTS AND COMPOUNDS - anything that has mass and takes up space. - cannot be broken down to other substances. - substance containing two or more different elements

More information

EXAM I COURSE TFY4310 MOLECULAR BIOPHYSICS December Suggested resolution

EXAM I COURSE TFY4310 MOLECULAR BIOPHYSICS December Suggested resolution page 1 of 7 EXAM I COURSE TFY4310 MOLECULAR BIOPHYSICS December 2013 Suggested resolution Exercise 1. [total: 25 p] a) [t: 5 p] Describe the bonding [1.5 p] and the molecular orbitals [1.5 p] of the ethylene

More information

Chapters 11 and 12: Intermolecular Forces of Liquids and Solids

Chapters 11 and 12: Intermolecular Forces of Liquids and Solids 1 Chapters 11 and 12: Intermolecular Forces of Liquids and Solids 11.1 A Molecular Comparison of Liquids and Solids The state of matter (Gas, liquid or solid) at a particular temperature and pressure depends

More information

Chapter-2 (Page 22-37) Physical and Chemical Properties of Water

Chapter-2 (Page 22-37) Physical and Chemical Properties of Water Chapter-2 (Page 22-37) Physical and Chemical Properties of Water Introduction About 70% of the mass of the human body is water. Water is central to biochemistry for the following reasons: 1- Biological

More information

Atoms can form stable units called molecules by sharing electrons.

Atoms can form stable units called molecules by sharing electrons. Atoms can form stable units called molecules by sharing electrons. The formation of molecules is the result of intramolecular bonding (within the molecule) e.g. ionic, covalent. Forces that cause the aggregation

More information

Molecular Forces in Biological Systems - Electrostatic Interactions; - Shielding of charged objects in solution

Molecular Forces in Biological Systems - Electrostatic Interactions; - Shielding of charged objects in solution Molecular Forces in Biological Systems - Electrostatic Interactions; - Shielding of charged objects in solution Electrostatic self-energy, effects of size and dielectric constant q q r r ε ε 1 ε 2? δq

More information

Chem 321 Lecture 11 - Chemical Activities 10/3/13

Chem 321 Lecture 11 - Chemical Activities 10/3/13 Student Learning Objectives Chem 321 Lecture 11 - Chemical Activities 10/3/13 One of the assumptions that has been made in equilibrium calculations thus far has been to equate K to a ratio of concentrations.

More information

Rama Abbady. Zina Smadi. Diala Abu-Hassan

Rama Abbady. Zina Smadi. Diala Abu-Hassan 1 Rama Abbady Zina Smadi Diala Abu-Hassan (00:00) (10:00) Types of Molecules in the Cell 1. Water Molecules: a large portion of the cell mass is water (70% of total cell mass). 2. Organic molecules (carbon

More information

Electrolyte Solutions

Electrolyte Solutions Chapter 8 Electrolyte Solutions In the last few chapters of this book, we will deal with several specific types of chemical systems. The first one is solutions and equilibria involving electrolytes, which

More information

Biochemistry,530:,, Introduc5on,to,Structural,Biology, Autumn,Quarter,2015,

Biochemistry,530:,, Introduc5on,to,Structural,Biology, Autumn,Quarter,2015, Biochemistry,530:,, Introduc5on,to,Structural,Biology, Autumn,Quarter,2015, Course,Informa5on, BIOC%530% GraduateAlevel,discussion,of,the,structure,,func5on,,and,chemistry,of,proteins,and, nucleic,acids,,control,of,enzyma5c,reac5ons.,please,see,the,course,syllabus,and,

More information

There are two types of polysaccharides in cell: glycogen and starch Starch and glycogen are polysaccharides that function to store energy Glycogen Glucose obtained from primary sources either remains soluble

More information

Intermolecular and Intramolecular Forces. Introduction

Intermolecular and Intramolecular Forces. Introduction Intermolecular and Intramolecular Forces Introduction Atoms can form stable units called molecules by sharing electrons. The formation of molecules is the result of intramolecular bonding (within the molecule)

More information

Chapter 13: Phenomena

Chapter 13: Phenomena Chapter 13: Phenomena Phenomena: Scientists measured the bond angles of some common molecules. In the pictures below each line represents a bond that contains 2 electrons. If multiple lines are drawn together

More information

The Biochemistry of Water

The Biochemistry of Water The Biochemistry of Water The Biochemistry of Water 2.3 Water, ph, and Buffers Water is the solvent of life All organisms are composed primarily of water, such that most eukaryotic organisms are about

More information

Topic 3 Periodicity 3.2 Physical Properties. IB Chemistry T03D02

Topic 3 Periodicity 3.2 Physical Properties. IB Chemistry T03D02 Topic 3 Periodicity 3.2 Physical Properties IB Chemistry T03D02 3.1 Physical Properties hrs 3.2.1 Define the terms first ionization energy and electronegativity. (1) 3.2.2 Describe and explain the trends

More information

Big Idea: Ionic Bonds: Ionic Bonds: Metals: Nonmetals: Covalent Bonds: Ionic Solids: What ions do atoms form? Electron Electron

Big Idea: Ionic Bonds: Ionic Bonds: Metals: Nonmetals: Covalent Bonds: Ionic Solids: What ions do atoms form? Electron Electron Chapter 13: Phenomena Phenomena: Scientists measured the bond angles of some common molecules. In the pictures below each line represents a bond that contains 2 electrons. If multiple lines are drawn together

More information

BIBC 100. Structural Biochemistry

BIBC 100. Structural Biochemistry BIBC 100 Structural Biochemistry http://classes.biology.ucsd.edu/bibc100.wi14 Papers- Dialogue with Scientists Questions: Why? How? What? So What? Dialogue Structure to explain function Knowledge Food

More information

BCMP 201 Protein biochemistry

BCMP 201 Protein biochemistry BCMP 201 Protein biochemistry BCMP 201 Protein biochemistry with emphasis on the interrelated roles of protein structure, catalytic activity, and macromolecular interactions in biological processes. The

More information

- intermolecular forces forces that exist between molecules

- intermolecular forces forces that exist between molecules Chapter 11: Intermolecular Forces, Liquids, and Solids - intermolecular forces forces that exist between molecules 11.1 A Molecular Comparison of Liquids and Solids - gases - average kinetic energy of

More information

*blood and bones contain colloids. *milk is a good example of a colloidal dispersion.

*blood and bones contain colloids. *milk is a good example of a colloidal dispersion. Chap. 3. Colloids 3.1. Introduction - Simple definition of a colloid: a macroscopically heterogeneous system where one component has dimensions in between molecules and macroscopic particles like sand

More information

Lecture 2 and 3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability

Lecture 2 and 3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability Lecture 2 and 3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability Part I. Review of forces Covalent bonds Non-covalent Interactions: Van der Waals Interactions

More information

CHEMISTRY Topic #1: Atomic Structure and Nuclear Chemistry Fall 2017 Dr. Susan Findlay See Exercise 5.3

CHEMISTRY Topic #1: Atomic Structure and Nuclear Chemistry Fall 2017 Dr. Susan Findlay See Exercise 5.3 CHEMISTRY 1000 Topic #1: Atomic Structure and Nuclear Chemistry Fall 2017 Dr. Susan Findlay See Exercise 5.3 Periodic Trends and Effective Nuclear Charge Imagine four atoms/ions: One has a nucleus with

More information

File ISM04. Properties of Colloids I

File ISM04. Properties of Colloids I File ISM04 Properties of Colloids I 1 Colloids Small things, but much bigger than a molecule Background: Foundations of Colloid Science Vol I & II, R.J. Hunter Physical Chemistry, P.W. Atkins, Chapter

More information

Theoretische Physik 2: Elektrodynamik (Prof. A-S. Smith) Home assignment 11

Theoretische Physik 2: Elektrodynamik (Prof. A-S. Smith) Home assignment 11 WiSe 22..23 Prof. Dr. A-S. Smith Dipl.-Phys. Matthias Saba am Lehrstuhl für Theoretische Physik I Department für Physik Friedrich-Alexander-Universität Erlangen-Nürnberg Problem. Theoretische Physik 2:

More information

Introduction. Chapter Plasma: definitions

Introduction. Chapter Plasma: definitions Chapter 1 Introduction 1.1 Plasma: definitions A plasma is a quasi-neutral gas of charged and neutral particles which exhibits collective behaviour. An equivalent, alternative definition: A plasma is a

More information

1) Here we review the various types of interactions that can take place between and among molecules.

1) Here we review the various types of interactions that can take place between and among molecules. Chem 431A-L02-W'05 page 1 of 6 Chem 431A-L02-W'05 Summary of lecture topics discussed in lecture 2-3: 1) Here we review the various types of interactions that can take place between and among molecules.

More information

Lecture 2-3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability

Lecture 2-3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability Lecture 2-3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability Part I. Review of forces Covalent bonds Non-covalent Interactions Van der Waals Interactions

More information

Concept review: Binding equilibria

Concept review: Binding equilibria Concept review: Binding equilibria 1 Binding equilibria and association/dissociation constants 2 The binding of a protein to a ligand at equilibrium can be written as: P + L PL And so the equilibrium constant

More information

MOLECULES. ENERGY LEVELS electronic vibrational rotational

MOLECULES. ENERGY LEVELS electronic vibrational rotational MOLECULES BONDS Ionic: closed shell (+) or open shell (-) Covalent: both open shells neutral ( share e) Other (skip): van der Waals (He-He) Hydrogen bonds (in DNA, proteins, etc) ENERGY LEVELS electronic

More information

SAM Teacher s Guide Protein Partnering and Function

SAM Teacher s Guide Protein Partnering and Function SAM Teacher s Guide Protein Partnering and Function Overview Students explore protein molecules physical and chemical characteristics and learn that these unique characteristics enable other molecules

More information

The Chemical Context of Life

The Chemical Context of Life Elements and Compounds The Chemical Context of Life Sodium Chlorine! Sodium chloride! An element is a substance that cannot be broken down to other substances by chemical reactions A compound is a substance

More information

Definition of Matter. Subatomic particles 8/20/2012

Definition of Matter. Subatomic particles 8/20/2012 Interplay of Biology and Chemistry Here is a link to the video these beetles are fairly common locally an amazing adaptation, and a good example of chemistry and physics in biology. Also look for creationist-evolutionist

More information

Lecture Presentation. Chapter 8. Periodic Properties of the Element. Sherril Soman Grand Valley State University Pearson Education, Inc.

Lecture Presentation. Chapter 8. Periodic Properties of the Element. Sherril Soman Grand Valley State University Pearson Education, Inc. Lecture Presentation Chapter 8 Periodic Properties of the Element Sherril Soman Grand Valley State University Nerve Transmission Movement of ions across cell membranes is the basis for the transmission

More information

Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte

Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte THE JOURNAL OF CHEMICAL PHYSICS 122, 044903 2005 Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte Zhi-Jie Tan and Shi-Jie Chen a) Department of Physics and

More information

Chemical bonding in solids from ab-initio Calculations

Chemical bonding in solids from ab-initio Calculations Chemical bonding in solids from ab-initio Calculations 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India & Center for Materials Science and Nanotechnology, University

More information

Chapter 12 Intermolecular Forces and Liquids

Chapter 12 Intermolecular Forces and Liquids Chapter 12 Intermolecular Forces and Liquids Jeffrey Mack California State University, Sacramento Why? Why is water usually a liquid and not a gas? Why does liquid water boil at such a high temperature

More information

8.333: Statistical Mechanics I Problem Set # 5 Due: 11/22/13 Interacting particles & Quantum ensembles

8.333: Statistical Mechanics I Problem Set # 5 Due: 11/22/13 Interacting particles & Quantum ensembles 8.333: Statistical Mechanics I Problem Set # 5 Due: 11/22/13 Interacting particles & Quantum ensembles 1. Surfactant condensation: N surfactant molecules are added to the surface of water over an area

More information

Chapter 13: Phenomena

Chapter 13: Phenomena Chapter 13: Phenomena Phenomena: Scientists measured the bond angles of some common molecules. In the pictures below each line represents a bond that contains 2 electrons. If multiple lines are drawn together

More information

When intermolecular forces are strong, the atoms, molecules, or ions are strongly attracted to each other, and draw closer together.

When intermolecular forces are strong, the atoms, molecules, or ions are strongly attracted to each other, and draw closer together. INTERMOLECULAR FORCES: THE FORCE BEHIND VARIOUS PROPERTIES WHY? Intermolecular forces are largely responsible for the properties of affinity, solubility, volatility, melting/ boiling point, and viscosity.

More information

MCB100A/Chem130 MidTerm Exam 2 April 4, 2013

MCB100A/Chem130 MidTerm Exam 2 April 4, 2013 MCBA/Chem Miderm Exam 2 April 4, 2 Name Student ID rue/false (2 points each).. he Boltzmann constant, k b sets the energy scale for observing energy microstates 2. Atoms with favorable electronic configurations

More information

Supporting Information for Lysozyme Adsorption in ph-responsive Hydrogel Thin-Films: The non-trivial Role of Acid-Base Equilibrium

Supporting Information for Lysozyme Adsorption in ph-responsive Hydrogel Thin-Films: The non-trivial Role of Acid-Base Equilibrium Electronic Supplementary Material (ESI) for Soft Matter. This journal is The Royal Society of Chemistry 215 Supporting Information for Lysozyme Adsorption in ph-responsive Hydrogel Thin-Films: The non-trivial

More information

Intermolecular Forces

Intermolecular Forces Intermolecular Forces Molecular Compounds The simplest molecule is H 2 : Increased electron density draws nuclei together The pair of shared electrons constitutes a covalent bond. Intermolecular Forces

More information

Molecular Mechanics, Dynamics & Docking

Molecular Mechanics, Dynamics & Docking Molecular Mechanics, Dynamics & Docking Lawrence Hunter, Ph.D. Director, Computational Bioscience Program University of Colorado School of Medicine Larry.Hunter@uchsc.edu http://compbio.uchsc.edu/hunter

More information

ATOMIC BONDING Atomic Bonding

ATOMIC BONDING Atomic Bonding ATOMIC BONDING Atomic Bonding Primary Bonds Secondary Bonds Ionic Covalent Metallic van der Waals 1. IONIC BONDING q 11 Na & 17 Cl These two ions are attracted to eachother by the electrostatic force developed

More information

Module 8: "Stability of Colloids" Lecture 37: "" The Lecture Contains: DLVO Theory. Effect of Concentration. Objectives_template

Module 8: Stability of Colloids Lecture 37:  The Lecture Contains: DLVO Theory. Effect of Concentration. Objectives_template The Lecture Contains: DLVO Theory Effect of Concentration file:///e /courses/colloid_interface_science/lecture37/37_1.htm[6/16/2012 1:02:12 PM] Studying the stability of colloids is an important topic

More information

Concepts of Chemical Bonding and Molecular Geometry Part 1: Ionic and Covalent Bonds. David A. Katz Pima Community College Tucson, AZ

Concepts of Chemical Bonding and Molecular Geometry Part 1: Ionic and Covalent Bonds. David A. Katz Pima Community College Tucson, AZ Concepts of Chemical Bonding and Molecular Geometry Part 1: Ionic and Covalent Bonds David A. Katz Pima Community College Tucson, AZ Chemical Bonds Three basic types of bonds: Ionic Electrostatic attraction

More information

Chem 3502/4502 Physical Chemistry II (Quantum Mechanics) 3 Credits Spring Semester Christopher J. Cramer. Lecture 30, April 10, 2006

Chem 3502/4502 Physical Chemistry II (Quantum Mechanics) 3 Credits Spring Semester Christopher J. Cramer. Lecture 30, April 10, 2006 Chem 3502/4502 Physical Chemistry II (Quantum Mechanics) 3 Credits Spring Semester 20056 Christopher J. Cramer Lecture 30, April 10, 2006 Solved Homework The guess MO occupied coefficients were Occupied

More information

Chapter 8. Periodic Properties of the Element

Chapter 8. Periodic Properties of the Element Chapter 8 Periodic Properties of the Element Mendeleev (1834 1907) Ordered elements by atomic mass Saw a repeating pattern of properties Periodic law when the elements are arranged in order of increasing

More information

Fundamental Principles to Tutorials. Lecture 3: Introduction to Electrostatics in Salty Solution. Giuseppe Milano

Fundamental Principles to Tutorials. Lecture 3: Introduction to Electrostatics in Salty Solution. Giuseppe Milano III Advanced School on Biomolecular Simulation: Fundamental Principles to Tutorials Multiscale Methods from Lecture 3: Introduction to Electrostatics in Salty Solution Giuseppe Milano Reference Rob Phillips,

More information

Introduction into Biochemistry. Dr. Mamoun Ahram Lecture 1

Introduction into Biochemistry. Dr. Mamoun Ahram Lecture 1 Introduction into Biochemistry Dr. Mamoun Ahram Lecture 1 Course information Recommended textbooks Biochemistry; Mary K. Campbell and Shawn O. Farrell, Brooks Cole; 7 th edition Instructors Dr. Mamoun

More information

Molecular Driving Forces

Molecular Driving Forces Molecular Driving Forces Statistical Thermodynamics in Chemistry and Biology SUBGfittingen 7 At 216 513 073 / / Ken A. Dill Sarina Bromberg With the assistance of Dirk Stigter on the Electrostatics chapters

More information

A Gentle Introduction to (or Review of ) Fundamentals of Chemistry and Organic Chemistry

A Gentle Introduction to (or Review of ) Fundamentals of Chemistry and Organic Chemistry Wright State University CORE Scholar Computer Science and Engineering Faculty Publications Computer Science and Engineering 2003 A Gentle Introduction to (or Review of ) Fundamentals of Chemistry and Organic

More information

General Physical Chemistry II

General Physical Chemistry II General Physical Chemistry II Lecture 13 Aleksey Kocherzhenko October 16, 2014" Last time " The Hückel method" Ø Used to study π systems of conjugated molecules" Ø π orbitals are treated separately from

More information